Why Quantum Computing ?
BOOLEAN ALGEBRA
Working with True and False
Boolean Variables and Operators
Truth Tables
Logic Gates
Logic Circuits
AND Gate
OR Gate
NOT Gate
Multiple Input Gates
Equivalent Circuits 1
Equivalent Circuits 2
Universal Gate NAND
Exclusive-OR
XOR for Assignment
XOR of Bit Sequences 1
XOR of Bit Sequences 2
Introduction to Cryptography
Cryptography with XOR
Shared Secret
Importance of Randomness
Breaking the Code
PROBABILITY
Predicting the Future
Probability of a Boolean Expression
Mutually Exclusive Events
Independent Events
Manipulating Probabilities with Algebra
P( Mutually Exclusive Events )
P( Independent Events )
Complete Set of MutEx Events
P( A OR B )
Worked Examples 1
Worked Examples 2
P( Bit Values )
Analysis with Venn Diagrams
Venn Diagram: P(A AND B)
Venn Diagram: P( A OR B )
Venn Diagram: P( NOT A )
Worked Examples 1
Worked Examples 2
Conditional Probability
Worked Examples
STATISTICS
Introduction to Statistics
Random Variables
Mapping Random Variables
Mean, Average, Expected Value, ...
Worked Examples 1
Worked Examples 2
Beyond Mean
Standard Deviation
Worked Examples
Combinations of Random Variables
Correlation
Analysis of Correlation
COMPLEX NUMBERS
Introduction to Complex Numbers
Imaginary i
Addition of Complex Numbers
Subtraction
Multiplication by a Real
Division by a Real
Complex Multiplication
Worked Examples
Complex Conjugate
Squared Magnitude
Complex Division
Worked Examples
Euler's Formula
Polar Form
Worked Examples
Fractional Powers
Complex Cube Roots of 1
Square Root of i
2D Coordinates
LINEAR ALGEBRA
Introduction to Matrices
Matrix Dimensions
Matrix Addition
Matrix Subtraction
Scalar Multiplication
Matrix Multiplication
Worked Examples 1
Worked Examples 2
3x3 Example
Worked Examples 1
Worked Examples 2
When is Multiplication Possible?
Worked Examples
Not Commutative
Associative and Distributive
Dimension of Result
Odd Shaped Matrices
Worked Examples 1
Worked Examples 2
Worked Examples 3
Inner Product
Worked Examples
Identity Matrix
Matrix Inverse
Transpose
Worked Examples
Transpose of Product
Complex Conjugate of Matrices
Adjoint
Unitary
Hermitian
Hermitian and Unitary
Why Hermitian or Unitary ?
Vectors and Transformations
Rotation in 2D
Special Directions
Eigen Vectors and Eigen Values
More Eigen Vectors
Dirac Bra-ket Notation
QUBITS AND SUPERPOSITION
From Bits to Qubits
Polarized Photons of Light
Photons and Polarizing Filters
More on Photons and Polarizing Filters
Filters Change Polarization
Quantum Behavior of Polarizers
Polarizing Single Photons
Using Calcite
Loss of Information
Finding Angle of Polarization
Finding Polarization of a Single Photon
Limitations of Measurement
Repeated Measurement 1
Repeated Measurement 2
Repeated Measurement with Filters
Running the Java Code
Simulation of Classical Bit
Simulation of Qubit (Quantum Bit)
No Cloning Theorem 1
No Cloning Theorem 2
Measurement is Irreversible
Deterministic vs Probabilistic
Simulating Measurements
Superposition
Collapse of Superposition
Conclusion